Inductance of a single-layer close-wound air-cored coil.
Calculations to give the inductance of a single-layer close-wound air-cored coil are extremely complex, but a good approximation is given by the following formula provided that these assumptions are adhered to:
Wire diameter is less than 10% of the coil diameter.
Wire is close wound in a single layer.
The coil's length is 0.4 to 3 times the diameter.
The formula is often called Wheeler's Formula .. (see picture below) ..
Where:
L=inductance, in uH
d=coil diameter, in inches
b=coil length, in inches
N=number of turns